Jobs on HPC clusters can suffer significant performance degradation due to inter-job network interference. Approaches to mitigating this interference primarily focus on reactive routing schemes. A better approach - -in that it completely eliminates inter-job interference - -is to implement scheduling policies that proactively enforce network isolation for every job. However, existing schedulers that allocate isolated partitions lead to lowered system utilization, which creates a barrier to adoption. Accordingly, we design and implement Jigsaw, a new job-isolating scheduling approach for three-level fat-trees that overcomes this barrier. Jigsaw typically achieves system utilization of 95-96%, while guaranteeing dedicated network links to jobs. In scenarios where jobs experience even modest performance improvements from interference-freedom, Jigsaw typically leads to lower job turnaround times and higher throughput than traditional job scheduling. To the best of our knowledge, Jigsaw is the first scheduler to eliminate inter-job network interference while maintaining high system utilization, leading to improved job and system performance.